y = -2x + 3

Now insert -2 through 4 where the x is located in the equation y = -2x + 3

and get the value of y

x = -2

y = -2x + 3

y = -2(-2) + 3

y = 4 + 3

y = 7

**First point = (x, y) = (-2,7)**

x = -1

y = -2x + 3

y = -2(-1) + 3

y = 2 + 3

y = 5

**Second point = (x, y) = (-1,5)**

x = 0

y = -2x + 3

y = -2(0) + 3

y = 0 + 3

y = 3

**Third point = (x, y) = (0,3)**

x = 1

y = -2x + 3

y = -2(1) + 3

y = -2 + 3

y = 1

**Forth point = (x, y) = (1,1)**

x = 2

y = -2x + 3

y = -2(2) + 3

y = -4 + 3

y = -1

**Fifth point = (x, y) = (2,-1)**

x = 3

y = -2x + 3

y = -2(3) + 3

y = -6 + 3

y = -3

**Sixth point = (x, y) = (3,-3)**

x = 4

y = -2x + 3

y = -2(4) + 3

y = -8 + 3

y = -5

**Seventh point = (x, y) = (4,-5)**

OK, now we have all our points, which you can see below:

(-2,7) (-1,5) (0,3) (1,1) (2,-1) (3,-3) (4,-5)

All there is left to do is plot our points on a graph and then draw a line through the points. The following picture demonstrates the concept.

]]>- The symbol means square root
- The symbol means the
**sum of**. - The
**x**equals our data. - The symbol means the average of the data.
- The
**n**represents how many we have in our data set, which we have**6**.

So lets find the average of the data below first.

(1) 28,995

(2) 37,534

(3) 31,361

(4) 27,087

(5) 20,966

(6) 37,741

We can find the standard deviation by breaking down the equation. Lets use a table so we can see what is going on.

Data (x) |
Data – Mean |
(Data – Mean) |

28,995 | 28,995 – 30614 = -1619 | |

37,534 | 37,534 – 30614 = 6920 | |

31,361 | 31,361 – 30614 = 747 | |

31,361 | 27,087 – 30614 = -3527 | |

20,966 | 20,966 – 30614 = -9648 | |

37,741 | 37,741 – 30614 = 7127 | |

Total: |
0 | 207383332 |

Ok, now that we have our totals for our data, we can use our standard deviation equation.

We have found the ,which is 207383332. We also know that n = 6 so we plug that in for n – 1, which would be 6 – 1 = 5. Now we just need to setup our equation by plugging in the numbers.

WOW, that was a little bit of work to find the standard deviation by hand. Best to use a calculator or some other tool such as cocalc.com and python.

]]>